Yep I reported that injury bug , but you weirdos didn't think 6 of 8 injuries in the first quarter could be considered a bug.
I'm going to probably go deeper into the math than either of us would like, so feel free to look for the "LOOK HERE!" and just start reading from there, but if you're interested in actually understanding, here goes.
Let's assume that OT is not involved, and that each injury has an equal chance of occurring in each of the four quarters. Seems reasonable enough, right? There may be other factors we don't know of but this should be a good enough baseline. So the chances of any given injury occurring in the first quarter specifically are 1 in 4.
For this to happen six of eight times, we first need to figure out how many distinct outcomes there are - which is 4 to the 8th power, which would be the same as 16 to the fourth or 256 squared, or 65536. So if we pick a number randomly from 1 to 4 a total of eight times, and represented it with an 8-digit number, it could be for example:
11111111
Which would represent 8 straight first quarter injuries.
Now, there is only 1 way to come up with 8 ones, so that's a single occurrence. To have 7 of the 8 be ones, there are 24 different combinations (8 different choices for the non-1 digit, times 3 different options). For 6 of 8 to be ones, it's a little more complicated - there are 28 distinct pairs of digits to choose from (8 for the first, 7 for the second, divided by two because order doesn't matter) and then 9 different combinations for those two digits to be non-1s, so a total of 252.
So adding it up, there are 1 + 24 + 252 = 277 different combinations to receive 6 or more 1st quarter injuries out of 8 consecutive injuries. When we divide 277 by 65536 ...
LOOK HERE!
The likelihood of you having at least six of your eight injuries be in the first quarter is 0.42%. Which means, in a game with 40,000 users, it would be reasonable to assume that this specific scenario or the harsher variants would happen to 169
users. So please understand that just because something is unlikely to happen to any one person, it doesn't mean that it's unlikely to happen at all and assume that if it affects you then it must be a bug.
(*) - Or 168 if we rounded the probability to the 0.42 before multiplying, which would be less accurate but should probably be pointed out so that extra user is accounted for.
Last edited by GM-hrudey at 2/13/2013 1:59:24 PM